Tensor hierarchy and generalized Cartan calculus in SL(3) × SL(2) exceptional field theory

Open Access
Regular Article - Theoretical Physics

Abstract

We construct exceptional field theory for the duality group SL(3) × SL(2). The theory is defined on a space with 8 ‘external’ coordinates and 6 ‘internal’ coordinates in the (3, 2) fundamental representation, leading to a 14-dimensional generalized spacetime. The bosonic theory is uniquely determined by gauge invariance under generalized external and internal diffeomorphisms. The latter invariance can be made manifest by introducing higher form gauge fields and a so-called tensor hierarchy, which we systematically develop to much higher degree than in previous studies. To this end we introduce a novel Cartan-like tensor calculus based on a covariant nil-potent differential, generalizing the exterior derivative of conventional differential geometry. The theory encodes the full D = 11 or type IIB supergravity, respectively.

Keywords

M-Theory Differential and Algebraic Geometry Supergravity Models String Duality 

Notes

Open Access

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Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.Center for Theoretical PhysicsMassachusetts Institute of TechnologyCambridgeUnited States

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